solve and esxplan please>
A right triangle has acute angles measuring 2x+6 degrees and 3x−26 degrees. Use the Triangle Angle Sum Theorem to find the measures of the missing angles of the triangle.(
The Triangle Angle Sum Theorem states that the sum of the three interior angles in a triangle is always 180 degrees.
In this right triangle, one angle is a right angle and measures 90 degrees. Let's denote the measure of the first acute angle as 2x+6 degrees, and the measure of the second acute angle as 3x−26 degrees.
So, we have:
90 degrees + (2x+6) degrees + (3x−26) degrees = 180 degrees
90 + 2x + 6 + 3x - 26 = 180
90 + 2x + 3x + 6 - 26 = 180
5x + 70 = 180
5x = 110
x = 22
Now we can substitute the value of x back into the expressions for the angles:
First acute angle: 2(22) + 6 = 50 degrees
Second acute angle: 3(22) - 26 = 40 degrees
Therefore, the measures of the missing angles of the triangle are:
First acute angle: 50 degrees
Second acute angle: 40 degrees.